The self inductance of the primary winding of a single phase, $50$ Hz, transformer is $800$ mH, and that of the secondary winding is $600$ mH. The mutual inductance between these two windings is $480$ mH. The secondary winding of this transformer is short circuited and the primary winding is connected to a $50$ Hz, single phase, sinusoidal voltage source. The current flowing in both the windings is less than their respective rated currents. The resistance of both windings can be neglected. In this condition, what is the effective inductance (in mH) seen by the source?
1. $416$
2. $440$
3. $200$
4. $920$